Modelling Bee Foundation Mould
What you see here is automatic triangulation. You have quad faces in your model that are not planar and polygonal faces that are not planar cannot be printed so they are triangulated and since there is no way for a computer algorithm to determine where to insert the edges it sometimes fails to guess. 

The solution would be to enter edit mode with your object selected(tab) and use something like the knife tool(k) to triangulate the mesh manually so it fits your expectations. you can also join vertices with an edge by selecting 2 vertices and hitting j.